Optimised Heuristics for a Geodiverse RoutingProtocol

Yufei Cheng∗, M. Todd Gardner‡, Junyan Li∗, Rebecca May‡, Deep Medhi‡, and James P.G. Sterbenz∗†∗Information and Telecommunication Technology Center

EECS, The University of Kansas, Lawrence, KS, 66045, USA{yfcheng|balee|jpgs}@ittc.ku.edu

†SCC and InfoLab21, Lancaster LA1 4WA, UKjpgs@comp.lancs.ac.uk

www.ittc.ku.edu/resilinets‡University of Missouri-Kansas City, MO, USA

todd.gardner@faa.gov rm5x8@mail.umkc.edu DMedhi@umkc.edu

Abstract—We propose two heuristics for solving the pathgeodiverse problem (PGD), in which the calculation of a numberof geographically separated paths is required. The geodiversepaths can be used to circumvent physical challenges such as large-scale disasters in telecommunication networks. The heuristicswe propose for solving PGD have significantly less complexitycompared to the optimal algorithm we previously used whilestill performing well by returning multiple geodiverse paths foreach node pair. The geodiverse paths contribute to providingresilience against regional challenges. We present the GeoDivRProuting protocol with two new routing heuristics implemented,which provide the end nodes with multiple geographically diversepaths and demonstrates better performance compared to OSPFwhen the network is subject to area-based challenges.

Index Terms—path geodiversitiy; physical topology; survivablerouting heuristics; network resilience; diversity routing; multi-path routing;

I. INTRODUCTION AND MOTIVATION

Telecommunication networks rely heavily on physical in-frastructure such as optical fibers, amplifiers, routers, andswitches to maintain normal operation, and their resilience tovarious faults and challenges is important to be analysed [1].The geolocation of network components and their relative dis-tance between each other affect the network survivability sincea significant number of challenges affect a wide range of nodesand links. Most previous work considers only random link andnon-correlated failures [2], [3]. In contrast, we are modellingcorrelated failures and attacks [4]. It has also been observedthat a large number of failures in a geographical region cancause catastrophic damage to the network communications [5].We study the geodiversity characteristics of the network graphto understand how regional challenges affect connectivity ofthe network and how to mitigate its impact. Many area-basedchallenges can be modelled as a circular area with a certainchallenge radius. For example, an earthquake or hurricanethat has a challenged radius of 0 to 500 miles impact zonecan cause failed links and nodes with substantial impact onnetwork communications [6].

We have proposed a two-step optimal algorithm for solvingthe path geodiverse problem (PGD). The algorithm begins

with the Suurballe’s algorithm [7], [8] in which a shortest-pathalgorithm (SPA) is iteratively applied. After each iteration ofthe SPA, the weight of the edges from the constructed path isadjusted by adding a penalty factor. Once the algorithm hasidentified k paths, it selects the path with distance d separa-tion (in which any two nodes on disjoint paths are separated bygreater than d distance) by iteratively comparing the distancebetween each and every node pair from all the candidate paths.Based on our algorithm, we have designed a geodiverse routingprotocol (GeoDivRP) that uses the geographic location ofnodes and routes traffic around the challenges by exploiting thediversity in the underlying physical topologies [5]. This mech-anism reaches optimality in choosing the best d-separationpaths assuming a large number of candidate paths. However,as SPA is applied k times for generating the candidate pathsbefore selecting the qualified ones, its time complexity is largeand the computation is slow. To reduce the complexity ofthe optimal algorithm, we propose two heuristics, iterativeWayPoint Shortest Path heuristic (iWPSP) and Modified LinkWeight heuristic (MLW). We approach these two heuristicsfrom different perspectives: iWPSP selects one waypoint nodeand performs SPA twice between the waypoint node andsource neighbor node, and then the waypoint node and destina-tion neighbor node, respectively. On the other hand, our secondheuristic MLW linearly or exponentially increases the links’weight within distance d from the straight line connectingsource and destination node. SPA is then used to calculate thepaths based on the modified link weights. We use Dijkstra’sshortest path algorithm [9] for both heuristics.

Our GeoDivRP fits in the protocol stack as shown inFigure 1. Knobs K are used by higher layers to influencelower layer operation while dials D are the mechanisms forlower layers to provide feedback to higher layers [10]. Theapplication layer passes a service specification and threatmodel down to our resilient transport layer protocol ResTP.Upon receiving these parameters, ResTP determines the typeof transport service needed (including error control and mul-tipath characteristics) and requests that GeoDivRP calculategeodiverse paths that meet the requirement tuple (k, d, [h, t]),

path char

dials knobs

{ss, tm}

GeoDivRP

ResTP

App

{k,d,[h,t]}

K32

D74

D43

D32

Fig. 1. Layered block diagram of GeDivRP and ResTP

where k is the total number of geodiverse paths requested, d isthe distance separation criteria, [h, t] are the desired constraintson path stretch h and temporal skew across paths t. ResTP thenestablishes a multiflow with error control needed for meet theservice spec, including the per-subflow control (ARQ, hybridARQ, FEC, or none) and flow bundle (e.g. 2-of-3 erasure codefor real-time critical service, or 1+1 redundany with a hot-standby for delay and loss tolerant service) taking advantageof k d-geodiverse paths [P ] provided by GeoDivRP. We applythe multipath algorithm in the context of several real-worldservice provider networks to analyse the diversity gain andpacket delivery ratio when routing protocol is considered.We further extend this routing mechanism to our geo-diverserouting protocol GeoDivRP.

The remaining sections of the paper are organised as fol-lows: Section II presents the background and related work.Section III introduces our two routing heuristics and theevaluation methodology. Section IV presents the simulationresults and demonstrates the performance gain from ourrouting heuristics in real-world physical networks. Section Vconcludes the paper and suggests future work.

II. BACKGROUND

The transportation network community has been studyinggeographically diverse path algorithms [11]–[13] to reducedanger to populated areas when transporting hazardous mate-rials. However, similar to our optimal algorithm [5], their workrequires the calculation of k shortest paths. One exception isthe gateway shortest path algorithm [12]. It selects one gate-way node for a path gateway when calculating shortest path,

but has a couple of drawbacks. For example, it can easily formloops, and when calculating more than two geodiverse paths,the later calculated paths are less separated from the previousestablished path. This is because the gateway node is alwayschosen based on the distance to the absolute shortest path.Another work has presented a performance comparison of theexisting geodiverse algorithms in transportation networks [14].

The telecommunication network community has long beenstudying edge/vertex-disjoint paths and many previous workshave presented survivable network routing design using dis-joint paths [7], [8], [15]–[17]. However, those works aregenerally concerned with ensuring that components and linksdo not share the same location, rather than considering thed distance between them needed for a specified separationfor path geodiversity (PGD). As area-based challenges areimportant to analyse, an efficient algorithm is required tosolve the PGD problem. We have proposed one path diversitymechanism for qualifying the reliability of network flowsto characterise the network resilience [18], [19]. We haveextended this work to the analysis of geodiversity in physi-cal network topologies and proposed cTGGD (compensatedgeographical graph diversity) to characterise the geodiversityof different network topologies [5]. We have also proposed arouting protocol that takes advantage of the geodiversity in thenetwork topology and achieve resilience by providing multiplegeodiverse paths to different application scenarios.

III. MODEL DESCRIPTION

In this section, we define path geodiversity and proposetwo heuristics for efficiently calculating geographically diversepaths. Specifically, we consider the path geodiverse prob-lem (PGD), which involves obtaining a set of paths that ared distance separated from each with every vertex in differentdisjoint paths (d-separation). The proposed heuristics returna path tuple of (S,D) paths from the graph G = (V,E,w),where V is the vertex set, E is the edge set, and w is the linkweight set. Dijkstra(G,n) is the standard Dijkstra algorithmwe use to provide the shortest path.

A. Path Geodiversity

We define the geodiversity as how far two paths are sep-arated from each other in terms of geographic distance. Wepresent some necessary definitions as follows.

Path is defined as a vector that contains all the links L andintermediate nodes N from source S to destination D

P = L ∪N (1)

GeoPath diversity D(Pa) is defined as the distance betweenany node member of the vector Pa and that of the shortest path.As shown in Figure 2, node 0 is the source and node 2 is thedestination. The shortest path consists node 0-1-2. The greendotted line shows the path P1 and the diversity D(P1) equalsd, which is the shortest distance between any node pairs onthe disjoint paths (except for the source and destination). Theblue dotted line shows path P2 and its geodiversity D(P2) iszero since P2 shares node 1 with the shortest path.

0 1

4 3 5

2

D(P1) = d

D(P2) = 0 d

Fig. 2. Geographic diversity: distance d

Path stretch is defined as the hop counts of a given path PA

divided by the hop counts of the shortest path Ps

S = LPA/LPs

(2)

where we use the same definition from [16].In addition to these metrics and definitions, we list the graph

notations used in the paper as follows:• G(V,E,w): input graph ‖G‖ with a set of vertices V , a

set of edges E and weight of edges w• S: source node• D: destination node• Sn: neighbor node chosen by source node• Dn: neighbor node chosen by destination node• k: number of geodiverse path requested• d: distance separation between each and every node in

different disjoint paths• δ: delta distance when selecting waypoint node

B. Heuristics Introduction

In consideration of decreasing the complexity of geodiversepath calculation, we propose two heuristics: iterative WayPointShortest Path (iWPSP) and Modified Link Weight (MLW). Asshown in Figure 3 for the case when k = 3, iWPSP first selectsneighbor nodes Sk1 and Dk2 that are d distance separatedfrom source node S and destination node D, respectively(for simplicity in this presentation we assume that such nodesexist; otherwise the nodes with the greatest distance will bechosen, iterating until nodes d apart are located). Assumingthe straight link connecting S and D is L, iWPSP selectswaypoint nodes m′ and m′′ in the opposite direction that aredistance d + δ apart from the middle node m in the shortestpath, where the segment m′mm′′ interleaves with the shortestpath. Dijkstra’s algorithm is performed for the two branchesSkm′ and Dkm′ . By connecting the shortest path returned fromthe two branches, the heuristic obtains the first geodiversepath P1. The same mechanism repeats for waypoint nodem′′ for the second geodiverse path. The variable d is a user-chosen parameter based on a threat model for a challengeof distance d, and δ is experimentally chosen for differentnetwork topologies to increase the probability of the heuristicsuccessfully returning a d-separation path. The δ parameter isalso introduced to prevent the edges in each of the two pathsfrom interleaving and creating routing loops. By tweaking thevalue of δ, this heuristic can select a nearby waypoint node ifthe previous one fails running Dijkstra’s algorithm. The codeof iWPSP is shown in Algorithm 1.

Functions:Calculate k paths from S to D separated by distance dInput:Gi:= input graphS:= source nodeD:= destination nodek:= number of requested geodiverse pathd:= separation distance between the pathsδ:= delta distance when selecting waypoint nodeOutput:k number of geographically d distance separated pathsbegin

segment L connecting S and D, with its middlepoint m;choose neighbor node Sk, Dk that is at least ddistance from Sk−1, Dk−1, respectively;if k is odd number then

choose two nodes m1 and m2 that are separatedby d+ δ on each direction of L, where m1mm2

is perpendicular bisector of L;P1 = SourceTreeDS ← Dijkstra(D,S);k− = 3;

elsechoose two nodes m1 and m2 that are separatedby d/2 + δ on each direction of L, wherem1mm2 is perpendicular bisector of L;k− = 2;

endpm1S1

= SourceTreeS1m1← Dijkstra(m1, S1);

pm2S2= SourceTreeS2m2

← Dijkstra(m2, S2);pm1D1 = SourceTreeD1m1 ← Dijkstra(m1, D1);pm2D2 = SourceTreeD2m2 ← Dijkstra(m2, D2);while k > 0 do

segment L = newest established path;choose one node mk that is separated by distanced+ δ from L on the farther direction from theabsolute shortest path;pmkSk

= SourceTreemkSk← Dijkstra(mk, Sk);

pmkDk= SourceTreemkDk

← Dijkstra(mk, Dk);k− = 1;

endif k is odd number then

P2 = pm1S1 + pm1D1 ;P3 = pm2S2 + pm2D2 ;...Pk = pmk−1Sk−1

+ pmk−1Dk−1;

elseP1 = pm1S1

+ pm1D1;

P2 = pm2S2 + pm2D2 ;...Pk = pmkSk

+ pmkDk;

endreturn (P1, P2, ..., Pk)

endAlgorithm 1: Iterative waypoint shortest path heuristic

>d

k = 3 >d+𝛿

>d

>d

>d

>d+𝛿

𝑆𝑘1

𝑆𝑘2

𝐷𝑘1

𝐷𝑘2

𝐷 𝑆 𝑚

𝑚′

𝑚′′

Fig. 3. Iterative waypoint shortest path heuristic

Fig. 4. Geodiverse paths by MLW heuristic in Grid network

Our second heuristic MLW statistically modifies the linkweights and performs Dijkstra’s algorithm to calculate thegeodiverse path with the modified link weights in the network.The heuristic begins by increasing, linearly or squarely, theweight in one direction based on the perpendicular distanceto the line L connecting source node S and destination nodeD. The weight incremental ratio is inversely proportional tothe distance from L. Dijkstra’s algorithm is applied on thegraph with modified link weights. The heuristic repeats theprocess for the other perpendicular direction to L. This waythe heuristic can generate two paths that are geographicallyseparated. If more diverse paths are required, the heuristicselects one of the geodiverse paths established as the startingline for modifying link weights and iteratively generates kgeodiverse paths.

We use a 5×5 grid network to demonstrate the d-separationpaths calculated by MLW. As shown in Figure 4, MLWcalculates two paths that are separated by distance d bystatistically modifying link weights. Node 21 is the source andnode 3 is the destination. The d value is set as twice length ofedges in the grid. iWPSP heuristic generates same results whenusing the same setup and the mechanism is shown in Figure 3.The weight shown in different color is used for calculatingpaths in its representative colors. For example, when MLW iscalculating the path shown in blue solid links, the link weightis statistically modified by decreasing towards the top rightcorner of the Grid network. The detailed heuristic is presentedin Algorithm 2.

Functions:cost(L):= cost functionInput:Gi:= input graphWi:= link weightsS:= source nodeD:= destination nodek:= number of diverse paths requestedbuffer := distance buffer to increase link weightOutput:k number of paths that are geographically separated bydistance dbegin

straight line l connecting source S and destination Dif k is odd number then

P1 = SourceTreeDS ← Dijkstra(D,S);modify link weight linearly or squarely on onedirection perpendicular to line l until distance d;P2 = SourceTreeDS ← Dijkstra(D,S);repeat the process for the other direction;buffer = d;k− = 3;

elsemodify link weight linearly or squarely on onedirection perpendicular to line l until distanced/2;P1 = SourceTreeDS ← Dijkstra(D,S);repeat the process for the other direction;buffer = d/2;k− = 2;

endwhile k > 0 do

buffer += d;modify link weight linearly decreasing on onedirection perpendicular to line l until buffer;links beyond distance buffer, link weight = 1;Pk−1 = SourceTreeDS ← Dijkstra(D,S);repeat the process in the other direction;Pk = SourceTreeDS ← Dijkstra(D,S);k− = 1;

endreturn (P1, P2, ..., Pk)

endAlgorithm 2: Modified link weight shortest path heuristic

We have implemented both of the heuristics in ourGeoDivRP routing protocol first introduced in [5]. The twoheuristics are implemented as different options and take a user-provided switch to control which heuristic the routing protocoluses. The implementation is done using ns-3 [20], a popularnetwork simulator to analyse network protocols and challengesthrough simulation. We base this protocol on link state routingmethodology. At the beginning of the simulation, by obtainingnode locations from the link state update messages, we cal-culate the geodiverse paths and store them in the path cache

server. When the simulation begins, our protocol sends datatraffic using the paths from the cache. When a challenge occursin the network, our protocol responds to the challenge fasterthan OSPF (Open Shortest Path First) [21] and calculates thepaths according to the challenge estimation [5]. The distancevalue d is a user-provided value, and when challenges occur,users can modify d according to the different threat models toensure the traffic circumvents the challenged area.

Both of the heuristics have incorporated improvement mech-anisms. When the calculated paths obtained fail to qualify thed-separation criteria, iWPSP will choose another waypoint thathas a slightly larger d distance, while MLW will increase thelink weight around the avoidance line. Then the heuristics ini-tialise another iteration of Dijkstra’s algorithm. The heuristicsfall back to the optimal algorithm if the result still does notqualify, which ensures that both of the heuristics have a betterchance acquiring the geodiverse path while not generatingtheir worst case complexity. Another major component of bothheuristics is loop detection. For example, the iWPSP algorithmcan create routing loops when calculating paths for cornernodes in the topology. We use a loop detection algorithmso that if a previous node from one path is identified, thealgorithm deletes that part.

IV. REAL NETWORK RESULTS

In this section, we evaluate the proposed heuristics andcompare their performance with the two-step optimal algo-rithm [5]. We present the geodiverse paths calculated byour heuristics using the Nobel-EU (Pan-European ReferenceNetwork) with 28 nodes and 40 links [22]. We assume achallenge along the line from Amsterdam to Rome with aradius of 50 km. Node Strasbourg and Frankfurt are in thechallenge circle. The result of iWPSP is shown in Figure 5.The challenge area is shown in the red circle. The result ofMLW is shown in Figure 6 for its two paths. We only showthe two paths from Amsterdam to Rome. The first path shownin red dashed link is Amsterdam-Hamburg-Berlin-Munich-Vienna-Zagreb-Rome, and the second path shown in blue solidlink is Amsterdam-Brussels-Paris-Lyon-Rome. We shown alarge radius challenge in Figure 7.

A. Complexity Analysis and Evaluation

We analyse the complexity of the two heuristics comparedto the optimal algorithm. For simplicity, we examine thecomplexity for obtaining two d-separation paths and assumethe Fibonacci heap for Dijkstra’s algorithm. The optimalalgorithm starts by calculating k edge-disjoint paths usingSuurballe’s algorithm, which requires k iterations of Dijkstra’salgorithm. Dijkstra’s algorithm can be performed in timeO(m + n log n) on a graph with n vertices and m edges.Therefore, the same time complexity applies to each pathfor the Suurballe’s algorithm, which makes its complexityO(km + kn log n). After generating k disjoint paths, theoptimal algorithm demands choice of paths that qualify thedistance separation criteria. This process requires n2 time,which means the total complexity for the optimal algorithm is

10 5 0 5 10 15 20 25 3035

40

45

50

55

60

65

Dublin

Glasgow

LondonAmsterdam

Brussels

Paris

Bordeaux

Madrid

Lyon

Barcelona

Oslo

Copenhagen

Hamburg

Frankfurt

Strasbourg

Zurich

Milan

Stockholm

Berlin Warsaw

Prague

Munich ViennaBudapest

ZagrebBelgrade

Rome

Athena

Fig. 5. iWPSP heuristic in Nobel-EU network

Fig. 6. MLW heuristic in Nobel-EU network

m + n log n + kn2, or O(kn2). The number of edge-disjointpaths k is usually large to establish the algorithm’s optimality.For most application scenarios, k is chosen to be 1000 [12].Therefore, for a network with vertices less than 1000, thecomplexity of the optimal algorithm goes up to O(n3).

iWPSP has a complexity of 2c2n2 log n, where c is theaverage number of neighbors for vertices, the complexity forchoosing the waypoint node is O(n), where n represents thenumber of nodes, and 2n log n is for Dijkstra’s algorithmto calculate the two shortest paths. Therefore, the worstcase scenario is O(n2 log n) while the best case scenario isO(n log n). Most of the physical topologies have an averagedegree between two and three [23]. This means that c in ourcomplexity analysis is a small constant. This reduces the bestcase time complexity of iWPSP to O(n log n). The complexityof MLW is O(2n log n), which is the complexity for invokingDijkstra’s algorithm twice. The complexity for both of ourheuristics is much better than that of the optimal algorithm,which is O(n3).

We present the execution time of the heuristics to demon-strate their effectiveness compared to optimal algorithm in the

Fig. 7. MLW heuristic in Nobel-EU network with large radius

case of calculating two d-separation paths. The evaluation ison a Linux machine with 3.16GHz Core 2 Duo CPU with4GB memory. We use different dimensions of grid networks toanalyse the time complexity. The grid dimension ranges from3×3 to 11×11, which means the number of nodes varies from9 to 121. We show the time to calculate all the node pairs inthe topology. When calculating only one path pair that happensmore often in real-world scenarios, the time is exponentiallyless. As shown in Figure 8, the x-axis is grid dimension andthe y-axis is the log-level algorithm execution time in seconds.Both MLW and iWPSP algorithms show better execution timecompared to the optimal algorithm. For calculating all thepaths in 11×11 grid, MLW takes 20 s, iWPSP takes 65 s,while the optimal algorithm takes greater than 3000 s. We canobserve that iWPSP has greater execution time compared tothat of MLW. This is because of the extra time of Dijkstra’salgorithm and selecting qualifying waypoint nodes. However,we observe that when calculating geodiverse paths in real-world topologies, iWPSP is more efficient in calculating thepaths for node pair around the topology boundary. This isbecause by selecting waypoints based on a distance and a deltavalue, iWPSP has more control over the distance separatedfrom the two paths. One better algorithm might be combiningthe two heuristics in calculating one topology, and this will beanalysed in future work.

B. Routing Performance Comparison

We now present simulations using fiber-level topologiesincluding Sprint [23], Level 3 [24], Internet2 [25], and Telia-Sonera [26]. We carry out the simulation once for eachtopology since there is no randomness in a given providertopology. We use CBR (constant bit rate) traffic, sending fromeach node to all others at a data rate of one packet per second.There are three area-based challenges we have simulated.From 20 to 40 s, the challenge occurs around Los Angeles,from 60 to 80 s in Kansas City, while the last challenge occursat New York City from 100 to 120 s. The challenge locationscome from the flow robustness analysis [5], and our challenge

Alg

orith

m T

ime

[s]

Grid Dimension

optimal

iWPSP

MLW

1E-03

1E-02

1E-01

1E+00

1E+01

1E+02

1E+03

1E+04

3 4 5 6 7 8 9 10 11

Fig. 8. Complexity analysis and comparison

duration time is set as 20 seconds. We choose these differentchallenge areas so that the most vulnerable area is aroundKansas City, due to its high betweenness as a major fiberexchange point for the US. The next damage level is aroundNew York City. While it does not have many high-betweennessnodes, the network is dense and more nodes are challenged ina given radius. The least vulnerable among these big cities isaround Los Angeles. The radii of the challenge areas are 300km. By assuming the correct estimation of the challenge radiusand position, we compare our protocol’s performance withstandard OSPF in terms of PDR (packet delivery ratio) as wellas delay. Packet delivery ratio is the ratio of packets delivereddivided to total packets sent, while delay is the time it takesfor the data packet to travel end-to-end. We use all the samechallenge areas throughout the topologies for easy comparison.The iWPSP heuristic is used in the GeoDivRP for calculatingthe geodiverse paths. MLW achieves the same PDR and delayresult as iWPSP when the links are carefully modified to makesure paths calculated are d distance separated. Since ns-3 isan event-driven network simulator and the algorithm executiontime is not included in the simulation time, the delay in ns-3for both iWPSP and MLW is the same.

The Sprint physical network contains 77 nodes and 114links. The PDR result for the Sprint network is shown inFigure 10. We compare the performance of our GeoDivRPwith standard OSPF. The second challenge at Kansas City areahappens at 60 s and GeoDivRP shows substantial performanceimprovement compared to OSPF. The PDR of OSPF dropsto 75 percent and takes 10 s to converge while the time forGeoDivRP is within one second and the PDR only dropstwo percent before it converges. The paths calculated byGeoDivRP to bypass the challenge is shown in Figure 9. Thered circle shown in this figure is the challenges area. Thelast challenge occurs from 100 s to 120 s and the differencein PDR between OSPF and GeoDivRP is small, only aboutone percent. This is because the challenge at New York Cityhas little effect on the connectivity of this overall topology.The PDR for OSPF drops about one percent and takes tenseconds to recover, and there is no noticeable PDR drop for

Fig. 9. Sprint topology under regional challenges

PD

R

Simulation Time [s]

Sprint GeoDivRP

Sprint OSPF

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120 140 160

Fig. 10. Sprint PDR under regional challenges

our protocol. The first challenge happens at 20 s to 40 s andthere is no noticeable PDR drop for both of the protocols.This is due to the same reason as in New York City and thedamage is even less.

The delay analysis for Sprint network is shown in Figure 11.The reason that OSPF shows lower delay when the networkis under challenge compared to GeoDivRP is because most ofthe data packets during the challenge have been dropped andthe lost packets are not counted as delay; this is why there isa delay drop for OSPF before converging. Consider the firstchallenge in Figure 11, the delay for OSPF drops from 20to 30 s due to the packet drops, while GeoDivRP convergesand calculates geodiverse paths during that period of time andshows one second higher in delay. However, the extra delayis caused by extra path stretch due to routing packets aroundthe challenged area. We also notice one delay bump for OSPFright after the challenge is finished. For example, in Figure 11,from 40 to 50 s, there is one increase in delay for OSPF.The same happens at 80 to 90 s, and 120 to 130 s. This isbecause OSPF needs to converge again after the topology hasrecovered from the challenge. In contrast, for our protocol, theconvergence time is still one second and no noticeable delayincrease is recorded.

The Level 3 physical network contains 99 nodes and 132links. The PDR for the Level 3 network is shown in Figure 12.Since Level 3 shares geographical similarities to the Sprintnetwork, we observe a similar PDR result. The challenge atKansas City area reduces the PDR for OSPF significantly; itis even greater than for Sprint. This is because the Level 3

Del

ay [m

s]

Simulation Time [s]

Sprint GeoDivRP

Sprint OSPF

17.0

17.5

18.0

18.5

19.0

19.5

20.0

20.5

0 20 40 60 80 100 120 140 160

Fig. 11. Sprint delay under area-based challenges

PD

R

Simulation Time [s]

Level3 GeoDivRP

Level3 OSPF

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120 140 160

Fig. 12. Level 3 PDR under regional challenges

network lacks some of the nodes and links from Seattle to theChicago area and the challenge around the Kansas City areacauses more damage to the PDR. As shown in Figure 13 usingLevel 3 network. The similar challenge location as from theSprint network has caused more nodes and links to fail. Weare not showing the delay case for the Level 3 network as theyare similar to those of the Sprint network.

The Internet2 physical network contains 16 nodes and 24links. The PDR for the Internet2 network is shown in Fig-ure 14. The challenged PDR and delay show a similar trend.The first challenge does damage to the network connectivity

Fig. 13. Level 3 topology under regional challenges

PD

R

Simulation Time [s]

Internet2 GeoDivRP

Internet2 OSPF

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120 140 160

Fig. 14. Internet2 PDR under regional challenges

Del

ay [m

s]

Simulation Time [s]

Internet2 GeoDivRP

Internet2 OSPF

6.4

6.6

6.8

7.0

7.2

7.4

7.6

7.8

8.0

8.2

8.4

0 20 40 60 80 100 120 140 160

Fig. 15. Internet2 delay under regional challenges

and GeoDivRP converges within one second. The secondchallenge in Kansas City area causes OSPF to drop around tenpercent in PDR and takes 10 s to converge and return the PDRto normal. The Los Angeles challenge has small impact on thenetwork similar to the Sprint case. The delay analysis for theInternet2 network is shown in Figure 15. For the same reason,OSPF shows a lower delay compared to that of GeoDivRPduring challenges from 20 to 30 s, 60 to 70 s, and 100 to110 s.

The TeliaSonera physical network contains 18 nodes and21 links. The PDR for TeliaSonera is shown in Figure 16.The second challenge at Kansas City area drops the PDR forOSPF to around 50 percent. This significant drop is causedby two reasons. First, the Kansas City node is connectingmultiple nodes between the east and west coast. Second, theTeliaSonera network is very sparse so the damage from KansasCity node is greater than that for the other networks. However,GeoDivRP recovers from the damage in only one second andlimits the PDR drop within one percent. The PDR case for boththe second and third challenges are similar. At the same time,OSPF drops about one percent of total packets and recoversonly after 10 s. The delay analysis is shown in Figure 17. The

PD

R

Simulation Time [s]

TeliaSonera GeoDivRP

TeliaSonera OSPF

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120 140 160

Fig. 16. TeliaSonera PDR under regional challenges

Del

ay [m

s]

Simulation Time [s]

TeliaSonera GeoDivRP

TeliaSonera OSPF

8.0

9.0

10.0

11.0

12.0

13.0

14.0

15.0

0 20 40 60 80 100 120 140 160

Fig. 17. TeliaSonera delay under regional challenges

delay for OSPF is lower during challenges since the droppedpackets are not counted in delay analysis. We notice that thedelay increase after the challenge for OSPF at 80 to 90 sis larger than other challenge locations as well as the samechallenge location in other topologies. This is because OSPFis using a path with more path stretch before convergence.

V. CONCLUSION AND FUTURE WORK

We have proposed two geodiverse heuristics for efficientlysolving the path geodiverse problem (PGD): iWPSP (iterativeWayPoint Shortest Path) and MLW (Modified Link Weight).We have implemented both of the heuristics in ns-3 andverified their effectiveness in providing reliable paths in theface of area-based challenges. We have demonstrated theeffectiveness of the heuristics in calculating and choosingdifferent geographically diverse paths to meet the requirementsfrom higher layers and its efficiency in routing the datatraffic around the failure area. GeoDivRP shows significantimprovement in both packet delivery ratio compared to OSPFand has comparable delay. The two heuristics for GeoDivRPuse different mechanisms to calculate geodiverse paths. Bycarefully modifying the link weights, MLW is capable ofproviding one geodiverse path using one iteration of Dijkstra’s

algorithm. However, it is difficult to provide solutions whenthe paths required are for node pairs around the topologyboundary, and the choice of link weight need to be carefullyconsidered for different networks. On the other hand, iWPSPrequires one extra Dijkstra’s algorithm for each geodiversepath than MLW, therefore, it takes a bit greater time to executeand solve the PGD problem. However, by carefully selectingwaypoint node and the parameters d and δ, different topologiesare similar and iWPSP works better than MLW when dealingwith node pairs in topology boundaries.

For future work, we will implement these two heuristicsin a testbed to emulate its effectiveness in real-world routersand examine the mechanisms to incorporate our geodiverserouting protocol into the current Internet. We will extend thiswork to analyse how the geographic multi-path mechanismimproves flow robustness. We will further extend this workto wireless networks and wired-wireless hybrid networks. Wewill incorporate our protocol with ResTP to test the protocolstack and analyse the protocol performance with multiple geo-diverse paths. We will fully analyse the relative benefits of thetwo heuristics and their combination, and enable GeoDivRP toautomatically choose different heuristics in different networktopologies.

ACKNOWLEDGMENTS

The authors would like to thank the members of the Re-siliNets group for discussions which led to this work. Thisresearch was supported in part by NSF grant CNS-1219028and CNS-1217736 (Resilient Network Design for MassiveFailures and Attacks) at KU and UMKC.

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